Finite Group Databasebeta

← #19147679

Subgroups — #19147679

Order 5504.

380 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583634C211yesmaximal, characteristic, complemented
2#14583289C211yesmaximal, characteristic, complemented
3#14583286C211yesmaximal, characteristic, complemented
4#14583281C211yesmaximal, characteristic, complemented
5#14583121C211yesmaximal, characteristic, complemented
6#14583118C211yesmaximal, characteristic, complemented
7#14583114C211yesmaximal, characteristic, complemented
8#14583111C211yesmaximal, characteristic, complemented
9#14583094C211yesmaximal, characteristic, complemented
10#14583091C211yesmaximal, characteristic, complemented
11#14583030C211yesmaximal, characteristic, complemented
12#14582999C211yesmaximal, characteristic, complemented
13#14582997C211yesmaximal, characteristic, complemented
14C4×#10621882C211yesmaximal, characteristic, complemented
15C43×#559C211yesmaximal, characteristic, complemented
16C2×#10621885C2211yescharacteristic
17C2×#10621883C2211yescharacteristic
18C2×#10621883C2211yescharacteristic
19C2×#10621884C2211yescharacteristic
20C2×#10621884C2211yescharacteristic
21C2×#10621882C2211yescharacteristic
22C2×#10621882C2211yescharacteristic
23C2×#10621882C2211yescharacteristic
24C2×#10621882C2211yescharacteristic
25#13063322C2211yescharacteristic
26#13063314—21no—
27#13063313C2211yescharacteristic
28#13063313C2211yescharacteristic
29#13063310—21no—
30#13063310—21no—
31C4×Dic86C2211yescharacteristic
32C4×D172C2211yescharacteristic
33C4×D172C2211yescharacteristic
34#13063287—21no—
35#13063258C2211yescharacteristic
36C4⋊(C43⋊C8)C2211yescharacteristic
37C4⋊(C43⋊C8)C2211yescharacteristic
38C4⋊(C43⋊C8)C2211yescharacteristic
39#13063249C2211yescharacteristic
40#13063248C2211yescharacteristic
41#13063246C2211yescharacteristic
42#13063246C2211yescharacteristic
43#13063245C2211yescharacteristic
44#13063245C2211yescharacteristic
45#13063236C2211yescharacteristic
46#13063236C2211yescharacteristic
47C4×C43⋊C8C2211yescharacteristic
48#127×C43C2211yescharacteristic
49#124×C43—21no—
50#124×C43C2211yescharacteristic
51#124×C43C2211yescharacteristic
52#123×C43—21no—
53#123×C43—21no—
54C4×Q8×C43C2211yescharacteristic
55C4×Q8×C43C2211yescharacteristic
56C4×D4×C43—21no—
57C4×D4×C43C2211yescharacteristic
58C4×D4×C43C2211yescharacteristic
59C2×Q8×C43D411yescharacteristic
60C2×Q8×C43C2311yescharacteristic
61C2×D4×C43—21no—
62C2×D4×C43—21no—
63C2×D4×C43C2311yescharacteristic
64C2×D4×C43C2311yescharacteristic
65C22×C4×C43—21no—
66C22×C4×C43—21no—
67C2×D172—21no—
68C2×D172—21no—
69C2×D172C2311yescharacteristic
70C2×D172C2311yescharacteristic
71C2×C4×D43—21no—
72C2×C4×D43—21no—
73C2×Dic86C2311yescharacteristic
74C4⋊C4×C43—21no—
75C4⋊C4×C43D411yescharacteristic
76C4⋊C4×C43D411yescharacteristic
77C4⋊C4×C43D411yescharacteristic
78C4⋊C4×C43C2311yescharacteristic
79C22⋊C4×C43—21no—
80C22⋊C4×C43—21no—
81C22⋊C4×C43—21no—
82C22⋊C4×C43—21no—
83C22⋊C4×C43—21no—
84C22⋊C4×C43—21no—
85C42×C43—21no—
86C42×C43C2311yescharacteristic
87C42×C43C2311yescharacteristic
88C42×C43C2311yescharacteristic
89#10621885—41no—
90#10621884—22no—
91#10621884—41no—
92#10621883—22no—
93#10621883—41no—
94#10621882—22no—
95#10621882—41no—
96#10621882—41no—
97#10621882—41no—
98(C2×D43)⋊C4—21no—
99(C2×D43)⋊C4—21no—
100(C2×D43)⋊C4—21no—
101(C2×D43)⋊C4—21no—
102(C2×D43)⋊C4—21no—
103(C2×D43)⋊C4—21no—
104C4⋊Dic43C2311yescharacteristic
105Dic43⋊C4—21no—
106C4×Dic43—21no—
107C2×C43⋊C8C2311yescharacteristic
108C2×C43⋊C8C2311yescharacteristic
109C2×C43⋊C8C2311yescharacteristic
110C2×C43⋊C8C2311yescharacteristic
111C23×C43—21no—
112C23×C43—21no—
113C22×D43—21no—
114C22×D43—21no—
115Q8×C43—21no—
116Q8×C43—21no—
117Q8×C43—41no—
118D4×C43—21no—
119D4×C43—21no—
120D4×C43—21no—
121D4×C43—21no—
122D4×C43—42no—
123D4×C43—81no—
124C2×C4×C43—21no—
125C2×C4×C43—21no—
126C2×C4×C43—81no—
127C2×C4×C43—81no—
128C2×C4×C43C2×D411yescharacteristic
129C2×C4×C43C2×D411yescharacteristic
130C2×C4×C43C2×D411yescharacteristic
131C2×C4×C43C2×D411yescharacteristic
132C2×C4×C43C2×D411yescharacteristic
133C2×C4×C43C2×D411yescharacteristic
134C2×C4×C43C2411yescharacteristic
135C2×Dic43—21no—
136C2×Dic43—21no—
137D172—21no—
138D172—21no—
139D172—21no—
140D172—21no—
141D172—42no—
142D172—81no—
143C4×D43—81no—
144C4×D43—81no—
145Dic86—21no—
146Dic86—21no—
147C43⋊C8—21no—
148C43⋊C8—21no—
149C43⋊C8—21no—
150C43⋊C8#4112yes—
151C22×C43—41no—
152C22×C43—41no—
153C22×C43—41no—
154C22×C43—41no—
155C22×C43—41no—
156C22×C43—41no—
157C22×C43C22×D411yescharacteristic
158C2×D43—41no—
159C2×D43—41no—
160C2×D43—41no—
161C2×D43—41no—
162C2×D43—41no—
163C2×D43—41no—
164C4×C43—21no—
165C4×C43—21no—
166C4×C43—21no—
167C4×C43—21no—
168C4×C43—21no—
169C4×C43—21no—
170C4×C43—41no—
171C4×C43—41no—
172C4×C43C2×#4111yescharacteristic
173C4×C43H(5,𝔽2)11yescharacteristic
174Dic43—41no—
175Dic43—41no—
176#3403—431nomaximal, Sylow
177C2×C43—81no—
178C2×C43—81no—
179C2×C43#55011yescharacteristic
180C2×C43#57511yescharacteristic
181C2×C43#57611yescharacteristic
182D43—81no—
183D43—81no—
184#559—431no—
185#559D4311yescharacteristic, complemented
186#496—431no—
187#496—431no—
188#495—431no—
189#464—431no—
190#464—431no—
191#463—431no—
192#463—431no—
193#459—431no—
194#459—431no—
195#446—431no—
196#440—431no—
197#440—431no—
198C4×D8—431no—
199C43#340311yescharacteristic, complemented, Sylow
200C2×Q16—431no—
201C2×SD16—431no—
202C2×SD16—431no—
203C2×SD16—431no—
204C2×SD16—431no—
205C2×D8—431no—
206C2×D8—431no—
207C2×D8—431no—
208C2×D8—431no—
209#127—431no—
210#127C2×D4311yescharacteristic
211#124—21no—
212#124—431no—
213#124—431no—
214#124—861no—
215#124C2×D4311yescharacteristic
216#124C2×D4311yescharacteristic
217#123—21no—
218#123—21no—
219#123—861no—
220#123—861no—
221C4×Q8—431no—
222C4×Q8C2×D4311yescharacteristic
223C4×Q8C2×D4311yescharacteristic
224C4×D4—21no—
225C4×D4—431no—
226C4×D4—431no—
227C4×D4—861no—
228C4×D4C2×D4311yescharacteristic
229C4×D4C2×D4311yescharacteristic
230#107—431no—
231C4⋊C8—431no—
232C4⋊C8—431no—
233C4⋊C8—431no—
234#103—431no—
235#103—431no—
236#102—431no—
237#102—431no—
238#102—431no—
239#102—431no—
240#97—431no—
241#97—431no—
242C4×C8—431no—
243C2×Q8—431no—
244C2×Q8C22⋊D4311yescharacteristic
245C2×Q8C22×D4311yescharacteristic
246C2×D4—21no—
247C2×D4—21no—
248C2×D4—431no—
249C2×D4—431no—
250C2×D4—861no—
251C2×D4—861no—
252C2×D4C22×D4311yescharacteristic
253C2×D4C22×D4311yescharacteristic
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—861no—
257C22×C4—861no—
258Q16—1721no—
259SD16—862no—
260SD16—862no—
261SD16—1721no—
262SD16—1721no—
263D8—862no—
264D8—1721no—
265D8—1721no—
266D8—1721no—
267C2×C8—431no—
268C2×C8—431no—
269C2×C8—431no—
270C2×C8—431no—
271C4⋊C4—21no—
272C4⋊C4—431no—
273C4⋊C4—861no—
274C4⋊C4C22⋊D4311yescharacteristic
275C4⋊C4C22⋊D4311yescharacteristic
276C4⋊C4C22⋊D4311yescharacteristic
277C4⋊C4C22×D4311yescharacteristic
278C22⋊C4—21no—
279C22⋊C4—21no—
280C22⋊C4—21no—
281C22⋊C4—21no—
282C22⋊C4—21no—
283C22⋊C4—21no—
284C22⋊C4—861no—
285C22⋊C4—861no—
286C22⋊C4—861no—
287C22⋊C4—861no—
288C22⋊C4—861no—
289C22⋊C4—861no—
290C42—21no—
291C42—861no—
292C42C22×D4311yescharacteristic
293C42C22×D4311yescharacteristic
294C42C22×D4311yescharacteristic
295C23—21no—
296C23—21no—
297C23—861no—
298C23—861no—
299Q8—21no—
300Q8—21no—
301Q8—41no—
302Q8—861no—
303Q8—861no—
304D4—21no—
305D4—21no—
306D4—21no—
307D4—21no—
308D4—42no—
309D4—81no—
310D4—861no—
311D4—861no—
312D4—861no—
313D4—861no—
314D4—3441no—
315D4—1722no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—81no—
319C2×C4—81no—
320C2×C4—861no—
321C2×C4—861no—
322C2×C4—3441no—
323C2×C4—3441no—
324C2×C4C2×C22⋊D4311yescharacteristic
325C2×C4C2×C22⋊D4311yescharacteristic
326C2×C4C2×C22⋊D4311yescharacteristic
327C2×C4C2×C22⋊D4311yescharacteristic
328C2×C4C2×C22⋊D4311yescharacteristic
329C2×C4C2×C22⋊D4311yescharacteristic
330C2×C4C23×D4311yescharacteristic
331C8—432no—
332C8—861no—
333C8—861no—
334C8—861no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—1721no—
342C22—1721no—
343C22—1721no—
344C22—1721no—
345C22—1721no—
346C22—1721no—
347C22C22×C22⋊D4311yescharacteristic
348C4—21no—
349C4—21no—
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—41no—
355C4—41no—
356C4—1721no—
357C4—1721no—
358C4#41×D4311yescharacteristic
359C4#1306337111yescharacteristic
360C2—81no—
361C2—81no—
362C2—3441no—
363C2—3441no—
364C2#1458356811yescharacteristic
365C2#1458369711yescharacteristic
366C2#1458370211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#559C2
socleC22×C43C22×D4
hypercenter#559D43
hypocenterC43#3403
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #559

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #14583634C2semidirect
2. #14583289C2semidirect
3. #14583286C2semidirect
4. #14583281C2semidirect
5. #14583121C2semidirect
6. #14583118C2semidirect
7. #14583114C2semidirect
8. #14583111C2semidirect
9. #14583094C2semidirect
10. #14583091C2semidirect
11. #14583030C2semidirect
12. #14582999C2semidirect
13. #14582997C2semidirect
14. C4×#10621882C2semidirect
15. C43×#559C2semidirect
185. #559D43semidirect
199. C43#3403semidirect